${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$: A nearly antiferromagnetic Fermi liquid

We have carried out strong-coupling calculations using the Eliashberg formalism, which provide strong evidence for the description of the planar quasiparticles in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ as a nearly antiferromagnetic Fermi liquid. We show that when one takes into account the full structure (in frequency and momentum space) of the spin-fluctuation-induced interaction between quasiparticles, a superconducting transition temperature of 90 K is obtained with a dimensionless coupling constant, λ=0.402N(0)g=0.83, for a hole concentration of 0.25, a quasiparticle spectrum characterized by nearest-neighbor hopping, t=0.25 eV, and a spin-fluctuation spectrum determined by experiment. With a next-nearest-neighbor hopping, t’=-0.45t, the coupling required to obtain a ${\mathit{T}}_{\mathit{c}}$ of 90 K is reduced by some 10%. Strong-coupling calculations of the normal state, using these latter parameters, yield a resistivity that varies linearly with temperature, with a magnitude at 90 K of 62 μΩ cm, a frequency dependence of the optical conductivity in quantitative agreement with experiment for energies ≤0.1 eV, a quasiparticle spectrum characterized by a momentum-dependent wave-function renormalization constant, 0.4≤${\mathit{Z}}_{\mathbf{p}}$≤0.6, and a self-energy whose imaginary part is proportional to ω for energies up to 0.25 eV. We give a progress report on the extent to which a self-consistent description of the spin-fluctuation excitation spectrum can be found by taking χ(q,ω)=χ̃(q,ω)/[1-J(q)χ̃(q,ω)], where χ̃(q,ω) is the irreducible particle-hole susceptibility calculated for quasiparticles coupled to spin excitations whose spectrum is given by χ(q,ω) and J(q) is the effective spin-spin coupling.